If the yield of the reaction C7H6O3 + (CH3CO)2O - C9H8O4 + COOH is 83%, what mass of salicylic acid would be required to prepare 1.0 kg of aspirin?
Understand the Problem
The question involves a chemical reaction where salicylic acid is reacted to produce aspirin, and it asks for the mass of salicylic acid required to yield a specific mass of aspirin based on a given yield percentage.
Answer
$$ M_{\text{salicylic}} = \frac{M_{\text{aspirin}}}{\frac{Y_{\text{percent}}}{100}} $$
Answer for screen readers
To find the mass of salicylic acid required, use the formula:
$$ M_{\text{salicylic}} = \frac{M_{\text{aspirin}}}{Y} $$
where $Y = \frac{Y_{\text{percent}}}{100}$.
Steps to Solve
- Identify the mass of aspirin required
You are given the mass of aspirin you want to produce. Let’s denote this mass as $M_{\text{aspirin}}$.
- Determine the yield percentage
You need to recognize that the yield percentage tells us how much of the theoretical maximum is actually produced. This can be expressed as a decimal by dividing the yield percentage by 100. Let's denote the yield percentage as $Y_{\text{percent}}$. Thus, we can express it as:
$$ Y = \frac{Y_{\text{percent}}}{100} $$
- Calculate the theoretical mass of salicylic acid corresponding to the mass of aspirin
Using the yield formula, we rearrange it to find the theoretical mass of salicylic acid required ($M_{\text{salicylic}}$):
$$ M_{\text{salicylic}} = \frac{M_{\text{aspirin}}}{Y} $$
- Calculate the mass of salicylic acid needed
Now substitute the known values into the equation to find the mass of salicylic acid required.
To find the mass of salicylic acid required, use the formula:
$$ M_{\text{salicylic}} = \frac{M_{\text{aspirin}}}{Y} $$
where $Y = \frac{Y_{\text{percent}}}{100}$.
More Information
This approach allows for an efficient calculation of the reactant needed based on desired product mass and yield. Understanding yield is essential in chemical reactions as it reflects the efficiency of the process.
Tips
- Confusing the yield percentage with the actual production amount. Remember that yield tells you how much of the theoretical mass is produced, not the exact mass directly.
- Forgetting to convert the yield percentage into a decimal form before using it in calculations.
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